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Replacing Turing Tape with a Fractal Tape
Published in Anirban Bandyopadhyay, Nanobrain, 2020
Russel’s paradox and the magic of time crystals: One of the most beautiful parts of a single, unified time crystal extended from the smallest spatial dimension to the large, covered with clocks of the shortest time domain to the longest is that only 15 geometric shapes with 15 primes can sing it 99.99% accuracy. Humans sense 4D, some other sensors could read 11D, but the pattern of primes reaches saturation above 1012 clocks, then it begins counting in a new way, so, the properties of the properties is a set to it. The argument that the universe is a frequency fractal of primes and the consciousness is its music is an excellent example of Russel’s paradox where the properties of properties become an element of the set in its core, hence, the set theorem cannot explain the situation. Now, since Russel’s paradox sets in, all higher-order logic cannot be transformed into a second-order logic. In such systems, a set of oscillators decides the order of logic and if it is said 5, then all five orders of logic operate independently and co-operatively in a single system. Of course, we can determine from the coupling map which clock would trigger which order logic. These time crystals cannot be transformed into a set of a linear sequence of clocks.
Reasoning about Sensor Networks
Published in S. Sitharama Iyengar, Richard R. Brooks, Distributed Sensor Networks, 2016
Manuel Peralta, Supratik Mukhopadhyay, Ramesh Bharadwaj
Notice that ΨT is a second-order logic formula since we are quantifying over one function symbol and one relation symbol. Also, let us assume that we have a fixed SOLj module f0. By definition, f0 is a finite list of statements in Stat. Thence, we can logically express f0: U → Stat by a finite conjunction of equalities as it is expressed in the following: Φf≜ìi∈U∧f0(i)=Stati
Knowledge Sharing and Reuse
Published in Jay Liebowitz, The Handbook of Applied Expert Systems, 2019
Grüninger and Fox (1994) propose the use of motivating scenarios that present the problem as a story of problems or examples and a set of intuitive solutions to the scenario problem. A set of informal competency questions includes the questions that an ontology must be able to answer in natural language. Then, the set of informal competency questions are translated into a formal set of competency questions using first-order logic (or possibly second-order logic). This formal set is also used to evaluate extensions of the ontology.
AI-enabled Enterprise Information Systems for Manufacturing
Published in Enterprise Information Systems, 2022
Milan Zdravković, Hervé Panetto, Georg Weichhart
A logic-based approach to dynamic systems is the situation calculus (J. McCarthy and Hayes 1969). This is a formal approach that supports reasoning about actions and change. The approach supports reasoning about behaviour and the consequences of enacting a behaviour (Reiter 2001). The situation calculus builds on first-order logic and has elements of second-order logic. This can lead to computational complex reasoning.
Analysis and research on intelligent manufacturing medical product design and intelligent hospital system dynamics based on machine learning under big data
Published in Enterprise Information Systems, 2022
As shown in Table 1, on a two-dimensional coordinate axis, simple first-order logic can be expressed by a single perceptron, while second-order logic cannot be expressed. In order to solve the problem of inadequate expression ability of a single perceptron, a combination of multiple perceptrons can realise the segmentation of complex space.